Seems that I've just forgotten that the Kindle is basically a tiny Linux computer; and jailbreaking gives - at least basic - access to it, like rooting does with an Android device.
My problem also has to do with the fact, that via USB only the userspace /mnt/us/* is visible and thus can be inspected, copied and managed directly. And therefore I didn't know which basic Linux tools are actually preinstalled.
Well, I have console access (via Vlasoftsoft's cool launcher - I also used the filemanager from this collection to inspect the /var/* stuff), I'll give it a try. Thanks again.